Michael Snelling, 59, from York, was questioned by detectives after being arrested yesterday (Tuesday, May 13) on Tyneside at a home believed to belong to his mother.
Crime scene investigators spent another day at the property in Hollywell Road in North Shields, where a sniffer dog was taken into the house to assist the search.
It is believed the home belonged to Mr Snelling’s elderly mother, who suffers from dementia and was moved to a care home about four months ago.
A car was also seized at the address.
Mr Snelling is believed to be a former York University lab technician and held a position in a mental health charity. He is said to have travelled back to Tyneside most weekends to visit his mother.
Investigators were also at his home on Burnholme Grove in York, where police set up a forensics tent in the back garden of the house. A sniffer dog was also used at the scene.
A police spokesman said tonight: "North Yorkshire Police have released a 59-year-old man on conditional bail following his arrest yesterday (Tuesday, May 13) on suspicion of murdering Claudia Lawrence.
"Forensic searches at relevant properties are expected to continue for a number of days.
"Every effort will be made to minimise disruption to local residents and the public affected by this work.
"North Yorkshire Police would like to thank those people for their patience and understanding.
"As investigations continue with the possibility of further arrests to be made, all sections of the community and the media are reminded and encouraged to respect the rights of others, including those connected to the case."
Ms Lawrence went missing in York in March 2009. She was last seen after leaving work at Goodricke College, part of York University, on the afternoon of March 18.
Her family came from Darlington and later moved to Malton, North Yorkshire, where she was brought up.
Martin Dales, a family friend and spokesman for her father, Peter Lawrence, said they are now urging anyone who may have any information – however irrelevant they think it may be - to get in contact with the police.
He said: “People may have been reminded of things as a result of yesterday’s activities and also have information in any case they may not have thought relevant but every piece of information is relevant; let the police be the judge of how relevant it is.
"We want the message to go out to the public to really, really wrack their brains now this has happened.”
He said the shock of an arrest – the first in the five years Ms Lawrence has been missing – was naturally leaving Mr Lawrence feeling fragile.
“I think he’s feeling quite fragile and withdrawn today and he just wants to wait and see and that’s the natural thing to do," said Mr Dales.
"The news came out the blue a bit. Even though new evidence emerged from searching her home, it’s still a shock."
Anyone with information should contact North Yorkshire Police on 101, select option 1, and pass details to the Force Control Room. Quote “Claudia Lawrence” when passing on details.
Information can also be passed to the independent charity Crimestoppers anonymously on 0800 555 111, quoting “Claudia Lawrence, North Yorkshire Police”. Alternatively, go to www.crimestoppers-uk.org and fill in an Anonymous Online Form.